image: 
Kaggle Repository for this dataset is located at here
Predict heart disease in a patient from Cleveland Medical Center, OH, USA. Since this analysis and modeling covers risk to human life, it is important to maintain a high rate of identifying patients with heart disease (i.e True Positives, therefore high sensitivity) while maintaining a realistic error rate for those who do not have heart disease ( False Positives, redicting heart disease in a patient when there is none)
This database contains data about the factors related to heart disease. There are 14 attributes from Cleveland Clinic Foundation. The “target” field refers to the presence or high risk of heart disease in the subject.
Attribute Information:
## X age sex cp trestbps chol fbs restecg thalach exang oldpeak slope ca
## 1 1 63 1 3 145 233 1 0 150 0 2.3 0 0
## 2 2 37 1 2 130 250 0 1 187 0 3.5 0 0
## 3 3 NA 0 1 130 204 0 0 172 0 1.4 2 0
## 4 4 56 1 1 120 236 0 1 178 0 0.8 2 0
## 5 5 57 0 0 120 354 NA 1 163 1 0.6 2 0
## thal target
## 1 1 1
## 2 2 1
## 3 2 1
## 4 2 1
## 5 2 1## X age sex cp
## Min. : 1.0 Min. :29.00 Min. :0.0000 Min. :0.0000
## 1st Qu.: 76.5 1st Qu.:48.00 1st Qu.:0.0000 1st Qu.:0.0000
## Median :152.0 Median :56.00 Median :1.0000 Median :1.0000
## Mean :152.0 Mean :54.52 Mean :0.6832 Mean :0.9601
## 3rd Qu.:227.5 3rd Qu.:61.00 3rd Qu.:1.0000 3rd Qu.:2.0000
## Max. :303.0 Max. :77.00 Max. :1.0000 Max. :3.0000
## NA's :45 NA's :27
## trestbps chol fbs restecg
## Min. : 94.0 Min. :126.0 Min. :0.0000 Min. :0.0000
## 1st Qu.:120.0 1st Qu.:211.0 1st Qu.:0.0000 1st Qu.:0.0000
## Median :130.0 Median :240.0 Median :0.0000 Median :1.0000
## Mean :131.6 Mean :246.3 Mean :0.1429 Mean :0.5281
## 3rd Qu.:140.0 3rd Qu.:274.5 3rd Qu.:0.0000 3rd Qu.:1.0000
## Max. :200.0 Max. :564.0 Max. :1.0000 Max. :2.0000
## NA's :30
## thalach exang oldpeak slope
## Min. : 71.0 Min. :0.0000 Min. :0.00 Min. :0.000
## 1st Qu.:133.5 1st Qu.:0.0000 1st Qu.:0.00 1st Qu.:1.000
## Median :153.0 Median :0.0000 Median :0.80 Median :1.000
## Mean :149.6 Mean :0.3267 Mean :1.04 Mean :1.407
## 3rd Qu.:166.0 3rd Qu.:1.0000 3rd Qu.:1.60 3rd Qu.:2.000
## Max. :202.0 Max. :1.0000 Max. :6.20 Max. :2.000
## NA's :30
## ca thal target
## Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:2.000 1st Qu.:0.0000
## Median :0.0000 Median :2.000 Median :1.0000
## Mean :0.7294 Mean :2.314 Mean :0.5446
## 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:1.0000
## Max. :4.0000 Max. :3.000 Max. :1.0000
## ##
## 0 1
## 0.4554455 0.5445545##
## 0 1
## 0.3168317 0.6831683##
## 0 1
## 0.5507246 0.4492754##
## 0 1
## 0.25 0.75There are 64% values in the data set with no missing values. There are 11% missing values in age, 6% in fbs, 5% in slope, and 5% in cp.
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##
## Variables sorted by number of missings:
## Variable Count
## age 0.14851485
## fbs 0.09900990
## slope 0.09900990
## cp 0.08910891
## X 0.00000000
## sex 0.00000000
## trestbps 0.00000000
## chol 0.00000000
## restecg 0.00000000
## thalach 0.00000000
## exang 0.00000000
## oldpeak 0.00000000
## ca 0.00000000
## thal 0.00000000
## target 0.00000000Missing data is imputed using predictive mean matching with Mice. Predictive Mean Matching (PMM) is a semi-parametric imputation approach. It is similar to the regression method except that for each missing value, it fills in a value randomly from among the a observed donor values from an observation whose regression-predicted values are closest to the regression-predicted value for the missing value from the simulated regression model (Heitjan and Little 1991; Schenker and Taylor 1996). The PMM method ensures that imputed values are plausible; it might be more appropriate than the regression method (which assumes a joint multivariate normal distribution) if the normality assumption is violated (Horton and Lipsitz 2001, p. 246).
Missing data after imputation.
Dataset is now complete as shown below.
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##
## Variables sorted by number of missings:
## Variable Count
## X 0
## age 0
## sex 0
## cp 0
## trestbps 0
## chol 0
## fbs 0
## restecg 0
## thalach 0
## exang 0
## oldpeak 0
## slope 0
## ca 0
## thal 0
## target 0Correlation Matrix
Visualize with a correlation matrix how features are correlated with each other and with the target variable. No two features have a strong correlation (<50%).
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Pairwise Correlations
##
## 0 1
## 0.5507246 0.4492754##
## 0 1
## 0.25 0.75
Rate of heart disease increases with age over 60
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Higher cholesterol increases rate of heart disease. We don’t know if this is good (HDL) or bad (LDL) cholesterol or total cholesterol
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Of those subjects with fasting blood sugar > 120 mg/dl, majority have higher risk of heart disease
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Subjects with higher resting ECG have a higher prevalence of heart disease
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We use the Rosner Tests to identify outlier.
Outcomes are:
Visualize prepared data
Let’s attempt to reduce dimensionality of dataset with Principal Component Analysis (PCA).
We use two methods: 1. Spectral decomposition which examines the covariances / correlations between variables (princomp) 2. Singular value decomposition which examines the covariances / correlations between individuals (prcomp) While both methods can easily be performed within R, the singular value decomposition method (i.e., Q-mode) is the preferred analysis for numerical accuracy (R Development Core Team 2011).
Both show that first 7-12 features give us 80%-90% of the variance, and that no one variable is overbearing.
Due to the high number of principal components relative to input features, we are not reducing any dimensions using PCA
PRINCOMP: Notice that first 7 components represent 85% of the variance
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.537633 1.1207524 1.0275455 0.9485534 0.88678665
## Proportion of Variance 0.265996 0.1413152 0.1187878 0.1012262 0.08847241
## Cumulative Proportion 0.265996 0.4073112 0.5260990 0.6273252 0.71579763
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 0.85777369 0.65933913 0.59080520 0.52457814
## Proportion of Variance 0.08277801 0.04890883 0.03926975 0.03095921
## Cumulative Proportion 0.79857564 0.84748447 0.88675423 0.91771344
## Comp.10 Comp.11 Comp.12 Comp.13
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## Standard deviation 0.45024183 0.42583390 0.37802272 0.33988365
## Proportion of Variance 0.02278408 0.02038075 0.01606111 0.01298375
## Cumulative Proportion 0.93953170 0.95991245 0.97597356 0.98895732
## Comp.14
## Standard deviation 0.31344936
## Proportion of Variance 0.01104268
## Cumulative Proportion 1.00000000
PRCOMP: Notice that first 12 components represent 86% of the variance
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.540 1.1226 1.0292 0.9501 0.88825 0.85919 0.66043
## Proportion of Variance 0.266 0.1413 0.1188 0.1012 0.08847 0.08278 0.04891
## Cumulative Proportion 0.266 0.4073 0.5261 0.6273 0.71580 0.79858 0.84748
## PC8 PC9 PC10 PC11 PC12 PC13
## Standard deviation 0.59178 0.52545 0.44565 0.42617 0.38231 0.32784
## Proportion of Variance 0.03927 0.03096 0.02227 0.02037 0.01639 0.01205
## Cumulative Proportion 0.88675 0.91771 0.93998 0.96035 0.97674 0.98879
## PC14
## Standard deviation 0.31617
## Proportion of Variance 0.01121
## Cumulative Proportion 1.00000
Types of Logistic Regressio -Binary Logistic Regression The categorical response has only two 2 possible outcomes. Example: Spam or Not -Multinomial Logistic Regression Three or more categories without ordering. Example: Predicting which food is preferred more (Veg, Non-Veg, Vegan) -Ordinal Logistic Regression Three or more categories with ordering. Example: Movie rating from 1 to 5
p value is an important evaluation metric.p-value helps you to decide whether there is a relationship between two variables or not.
The smaller the p-value this mean the more confident you are about the existence of relationship between the two variables. The origins of p-values comes form hypothesis testing in statistics. In hypothesis testing, you have two hypothesis: H0 (called the null hypothesis ) : There is no relationship between the two variables. H1 (called the alternative hypothesis): There exist a relationship between the two variables.
If the p-value is less than small threshold (often 0.05 is used), then you can reject the null hypothesis H0, which means that you decide that there is a relationship between the two variables.
Looking at the p values the following variables are predictors of target variable
Evaluate and refine the model -
Compute average prediction for true outcomes TP are 78%, that is predicting presence of heart disease correctly 78% of the time TN are 26%, that is predicting no heart disease when there is none 26% of the time
##
## Call:
## glm(formula = target ~ age + sex + cp + trestbps + chol + fbs +
## restecg + thalach + exang + oldpeak + slope + ca, family = binomial,
## data = trainData)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4422 -0.3588 0.1597 0.4854 2.3002
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.6865 0.8106 0.847 0.397009
## age -0.4887 0.2563 -1.907 0.056579 .
## sex -1.7608 0.5116 -3.442 0.000578 ***
## cp 0.6577 0.2180 3.018 0.002548 **
## trestbps -0.4288 0.2120 -2.023 0.043058 *
## chol -0.4255 0.2445 -1.740 0.081816 .
## fbs 0.3893 0.6726 0.579 0.562792
## restecg 0.6065 0.4000 1.516 0.129446
## thalach 0.2833 0.2574 1.101 0.271035
## exang -1.1019 0.4682 -2.353 0.018608 *
## oldpeak -0.7465 0.2699 -2.766 0.005682 **
## slope 0.6164 0.4415 1.396 0.162670
## ca -0.9816 0.2314 -4.242 2.22e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 313.54 on 227 degrees of freedom
## Residual deviance: 158.16 on 215 degrees of freedom
## AIC: 184.16
##
## Number of Fisher Scoring iterations: 6## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.001613 0.156975 0.637273 0.552632 0.922450 0.999223## 0 1
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## 0.2624057 0.7854937
The accuracy of the test depends on how well the test separates the group being tested into those with and without the disease in question. Accuracy is measured by the area under the ROC curve. An area of 1 represents a perfect test; an area of .5 represents a worthless test. A rough guide for classifying the accuracy of a diagnostic test is the traditional academic point system:
.90-1 = excellent (A) .80-.90 = good (B) .70-.80 = fair (C) .60-.70 = poor (D) .50-.60 = fail (F)
##
## FALSE TRUE
## 0 24 12
## 1 8 31
##
## Call:
## roc.default(response = testData$target, predictor = lrtest.prob, plot = TRUE, col = "blue")
##
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## Data: lrtest.prob in 35 controls (testData$target 0) < 39 cases (testData$target 1).
## Area under the curve: 0.896
Higher ECG result predics heart disease
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Higher exercise induced angina predicts heart disease
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Lower depression during stress test predicts heart disease
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Overview A decision tree is a flowchart-like tree structure where an internal node represents feature(or attribute), the branch represents a decision rule, and each leaf node represents the outcome. The topmost node in a decision tree is known as the root node. It learns to partition on the basis of the attribute value. It partitions the tree in recursively manner call recursive partitioning. This flowchart-like structure helps you in decision making. It’s visualization like a flowchart diagram which easily mimics the human level thinking. That is why decision trees are easy to understand and interpret.
Run the model against training data, predict target on test data
Evaluate the model -
ROC curve shows accuracy of this model is 82%
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##
## Call:
## roc.default(response = testData$target, predictor = factor(dt.predict, ordered = TRUE), plot = TRUE, col = "blue")
##
## Data: factor(dt.predict, ordered = TRUE) in 36 controls (testData$target 0) < 39 cases (testData$target 1).
## Area under the curve: 0.7179Overview
Run the model against training data, predict target on test data
Evaluate the model -
ROC curve shows accuracy of this model is 82%
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##
## Call:
## roc.default(response = testData$target, predictor = factor(annResult, ordered = TRUE), plot = TRUE, col = "blue")
##
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## Data: factor(annResult, ordered = TRUE) in 35 controls (testData$target 0) < 39 cases (testData$target 1).
## Area under the curve: 0.8216Gradient Boosting Machine (for Regression and Classification) is a forward learning ensemble method. The guiding heuristic is that good predictive results can be obtained through increasingly refined approximations. H2O’s GBM sequentially builds regression trees on all the features of the dataset in a fully distributed way - each tree is built in parallel.
Run the model against training data, predict target on test data
Evaluate the model -
ROC curve shows accuracy of this model is 86%
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##
## Call:
## roc.default(response = testData$target, predictor = gbm.test, plot = TRUE, col = "red")
##
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## Data: gbm.test in 35 controls (testData$target 0) < 39 cases (testData$target 1).
## Area under the curve: 0.8557##
## Call:
## roc.default(response = testData$target, predictor = gbm.test, plot = TRUE, col = "red")
##
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## Data: gbm.test in 35 controls (testData$target 0) < 39 cases (testData$target 1).
## Area under the curve: 0.8557